Free-form Method Research Articles

EVALUATION OF SUPERPLASTIC PROPERTIES OF AA7075 ALUMINUM ALLOY SHEET FABRICATED BY THERMOMECHANICAL PROCESSING

The superplastic forming (SPF) process is the large plastic deformation ability of metals and alloys. However, SPF ability can only be achieved under certain conditions including ultrafine grain (UFG) microstructure, high temperature, and very small strain rate. In this work, the high-strength aluminum alloy AA7075 was selected for the experimental process due to its outstanding industrial application. First, thermomechanical processing (TMP) is performed to create a fine stable grain size for the studied alloy. The UFG microstructure was obtained after TMP with an average grain size of about 10 μm. Subsequently, the tensile test method and the bulging free-forming (BFF) method were used to evaluate the superplastic properties of the AA7075 aluminum alloy sheet fabricated by TMP. These two methods are performed at temperatures of 500ºC and 530ºC with strain rates from 10-4 (s-1) to 10-3 (s-1). The relative elongation and the strain rate sensitivity are the evaluation criteria. At the temperature of 530ºC and strain rate of 10-3 (s-1), the maximum relative elongation and flow stress were achieved at 280% and 7.6 MPa, respectively. The value of the coefficient m ranges from 0.3 to 0.6. The obtained results confirm the SPF properties of the aluminum alloy sheet AA7075.

Multi-objective design optimization of a transonic axial fan stage using sparse active subspaces

In this paper, a multi-objective optimization strategy for efficient design of turbomachinery blades using sparse active subspaces is implemented for a turbofan stage design. The proposed strategy utilized sparse polynomial chaos expansion on a limited dataset to generate a function from which the differential and the covariance matrix can be obtained. Active subspace was used to compute the active variables via singular value decomposition and a hybrid polynomial correlated function expansion was used to construct a surrogate model on the active subspace. Coupled with freeform method and multi-objective genetic algorithm, an automated optimization loop was run at a single operating condition. An improvement in stage efficiency and total pressure ratio of 2.97% and 1.15% was achieved for the optimum design compared with the baseline. Additionally, total pressure loss coefficient decreased by 5.88%, exit flow angle by 34.65% and shock strength by 5.32%. The coupled effect of change in stagger angle, forward sweep, forward lean, and chord length reduced the recirculation at the hub, and blockage at the shroud due the tip leakage flow by decreasing the blade loading. The threshold value hyperparameter was found to be the most influential and must be accurately determined.

The use of soluble resin for additive manufacturing of automotive industry prototypes

The article describes the method of producing car parts using the Freeform method (FIM). The injection process into a mold obtained by 3D printing was simulated and the surface condition of the finished product made of high-strength PEEK was assessed.

An excursion into the core of the cluster lens Abell 1689

ABSTRACT Abell 1689 is a well-studied cluster of galaxies and one of the largest gravitational lens systems ever observed. We have obtained a reconstruction of the cluster Abell 1689 using grale, a free-form lens inversion method that relies exclusively on the multiple image data. Non-inclusion of any data related to cluster member galaxies ensures an unbiased measure of the mass distribution, which is the most notable feature of free-form methods like grale. We used two different sets of multiple image systems from the available strong lensing data – one containing only the secure systems (107 images) and the other containing all available systems, only excluding some very non-secure systems (151 images). For the very well-constrained central ∼100 kpc region of the cluster, we made a detailed comparison of the grale reconstructed lensing mass and stellar mass retrieved by the Spectral Energy Distribution (SED) fitting software fast++. We found a light-unaccompanied mass peak in this region, whose existence, while tentative, is favoured by the distribution of nearby images that are local maxima in the Fermat potential. However, further tests, using different methodologies are needed to confirm the reality of this feature. If it is shown to be real, this light-unaccompanied mass peak is consistent with dark matter self-interaction cross-section σ ≲ 1 cm2 g−1, while being in tension with larger cross-sections.

Adjoint optimization of a multi-row transonic compressor based on an extended free-form method

The adjoint method plays an important role in the aerodynamic design of turbomachinery. However, most optimization objects are only local parts of the fluid domain in turbomachinery, such as blade or end-wall. In this study, a novel parameterization method is adopted in the adjoint optimization framework to merge all design spaces together and then a typical multi-row compressor, Stage 35, is optimized by the in-house adjoint optimizer, TurboSim_un. The adiabatic efficiency of STAGE 35 is improved by 1.7%. Results show that the intersection of shock wave and boundary layer is weakened and the performance in mainstream is significantly improved.

Shape, Resonant Frequency and Thermoelastic Dissipation Analysis of Free-Formed Microhemispherical Shells Based on Forming Process Modeling.

Free-form microhemispherical shell resonators have the advantages of high quality factor and mass production. The shape of microhemispherical shells created via this process is based on a single mold and is difficult to adjust, which affects the resonant frequency and quality factor. In this paper, a process analysis model is established through in-depth analysis of the process mechanism and flow of the free-forming method. Based on this model, the influence of the designed preforming parameters on the shape, resonant frequency and thermoelastic dissipation of the microhemispherical shell are analyzed in detail, providing theoretical guidance for parameter design. The results show that the depth and the ratio of internal to external pressure of the substrate’s annular groove affect the height and thickness of the microhemispherical shell, and the structural thickness affects the thickness of the microhemispherical shell; these in turn affect the resonant frequency and thermoelastic dissipation of the microhemispherical shell resonator. In addition, the inner diameter of the substrate’s annular groove mainly affects the radius of the support column of the microhemispherical shell, and the influence on the resonant frequency and thermoelastic dissipation of the resonator is relatively low.

MARS: A New Maximum-entropy-regularized Strong Lensing Mass Reconstruction Method

Free-form strong-lensing (SL) mass reconstructions typically suffer from overfitting, which manifests itself as false-positive small-scale fluctuations. We present a new free-form MAximum-entropy ReconStruction (MARS) method without the assumption that light traces mass (LTM). The MARS algorithm enables us to achieve excellent convergence in source positions (∼0.″001), minimize spurious small-scale fluctuations, and provide a quasi-unique solution independently of initial conditions. Our method is tested with the publicly available synthetic SL data FF-SIMS. The comparison with the truth shows that the mass reconstruction quality is on par with those of the best-performing LTM methods published in the literature, which have been demonstrated to outperform existing free-form methods. In terms of the radial mass profile reconstruction, we achieve <1% agreement with the truth for the regions constrained by multiple images. Finally, we apply MARS to A1689 and find that the cluster mass in the SL regime is dominated by the primary halo centered on the brightest cluster galaxy and the weaker secondary halo is also coincident with the bright cluster member ∼160 kpc northeast. Within the SL field, the A1689 radial profile is well described by a Navarro–Frenk–White profile with c 200 = 5.53 ± 0.77 and kpc, and we find no evidence that A1689 is overconcentrated.

Spatiotemporal Free-Form Registration Method Assisted by a Minimum Spanning Tree During Discontinuous Transformations.

The sliding motion along the boundaries of discontinuous regions has been actively studied in B-spline free-form deformation framework. This study focusses on the sliding motion for a velocity field-based 3D+t registration. The discontinuity of the tangent direction guides the deformation of the object region, and a separate control of two regions provides a better registration accuracy. The sliding motion under the velocity field-based transformation is conducted under the [Formula: see text]-Rényi entropy estimator using a minimum spanning tree (MST) topology. Moreover, a new topology changing method of the MST is proposed. The topology change is performed as follows: inserting random noise, constructing the MST, and removing random noise while preserving a local connection consistency of the MST. This random noise process (RNP) prevents the [Formula: see text]-Rényi entropy-based registration from degrading in sliding motion, because the RNP creates a small disturbance around special locations. Experiments were performed using two publicly available datasets: the DIR-Lab dataset, which consists of 4D pulmonary computed tomography (CT) images, and a benchmarking framework dataset for cardiac 3D ultrasound. For the 4D pulmonary CT images, RNP produced a significantly improved result for the original MST with sliding motion (p<0.05). For the cardiac 3D ultrasound dataset, only a discontinuity-based registration indicated activity of the RNP. In contrast, the single MST without sliding motion did not show any improvement. These experiments proved the effectiveness of the RNP for sliding motion.

Free-form Lens Model and Mass Estimation of the High-redshift Galaxy Cluster ACT-CL J0102-4915, “El Gordo”

Abstract We examine the massive colliding cluster El Gordo, one of the most massive clusters at high redshift. We use a free-form lensing reconstruction method that avoids making assumptions about the mass distribution. We use data from the RELICS program and identify new multiply lensed system candidates. The new set of constraints and free-form method provide a new independent mass estimate of this intriguing colliding cluster. Our results are found to be consistent with earlier parametric models, indirectly confirming the assumptions made in earlier work. By fitting a double gNFW profile to the lens model and extrapolating to the virial radius, we infer a total mass for the cluster of M . We estimate the uncertainty in the mass due to errors in the photometric redshifts and discuss the uncertainty in the inferred virial mass due to the extrapolation from the lens model. We also find in our lens map a mass overdensity corresponding to the large cometary tail of hot gas, reinforcing its interpretation as a large tidal feature predicted by hydrodynamical simulations that mimic El Gordo. Finally, we discuss the observed relation between the plasma and the mass map, finding that the peak in the projected mass map may be associated with a large concentration of colder gas exhibiting possible star formation. El Gordo is one of the first clusters that will be observed with JWST, which is expected to unveil new high-redshift lensed galaxies around this interesting cluster and provide a more accurate estimation of its mass.

Simplified Geometric Approach to Freeform Beam Shaper Design

Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily. In order to keep these two quantities determined simultaneously, it is required to apply at least two powered refractive or reflective surfaces. In this paper, a fully geometric design method of double-freeform beam shapers is discussed briefly. The presented algorithm is based on two stages. First, integrable input-output ray mapping is calculated by the application of the novel GATMA (Geometric Approach to Monge–Ampere equation) method. It allows us to determine the shape of the first freeform surface. Then, according to the condition of constant optical path length between input and output plane, corrected by wavefront phases at those planes, the second surface is determined. GATMA algorithm combines advantages of Monge–Ampere (MA) equation and ray-tracing efficient apparatus. Compared to the state-of-the-art freeform design methods, GATMA does not need to solve MA equation directly but uses this equation as an error function. Such approach makes the computation algorithm simpler and more robust and convergent. The application of the proposed method in a challenging design example of a beam shaper, transforming uniform collimated beam into a beam having a triangular cross section and flat wavefront, is presented as a case study.

Constraining the abundance of dark matter in the central region of the galaxy cluster MACS J1206.2−0847 with a free-form strong lensing analysis

We performed a free-form strong lensing analysis of the galaxy cluster MACS J1206.2−0847 in order to estimate and constrain its inner dark matter distribution. The free-form method estimates the cluster total mass distribution without using any prior information about the underlying mass. We used 97 multiple lensed images belonging to 27 background sources and derived several models, which are consistent with the data. Among these models, we focus on those that better reproduce the radial images that are closest to the centre of the cluster. These radial images are the best probes of the dark matter distribution in the central region and constrain the mass distribution down to distances ∼7 kpc from the centre. We find that the morphology of the innermost radial arcs is due to the elongated morphology of the dark matter halo. We estimate the stellar mass contribution of the brightest cluster galaxy and subtracted it from the total mass in order to quantify the amount of dark matter in the central region. We fitted the derived dark matter density profile with a gNFW, which is characterised byrs= 167 kpc,ρs= 6.7 × 106 M⊙kpc−3, andγgNFW= 0.70. These results are consistent with a dynamically relaxed cluster. This inner slope is smaller than the cannonicalγ = 1 predicted by standard CDM models. This slope does not favour self-interacting models for which a shallower slope would be expected.

Parametric study on the aerodynamic performance of a ducted-fan rotor using free-form method

In this paper, the effects of various parameters, especially three engineering parameters (twist, sweep, lean), on aerodynamic and structural performance of the fan blade were investigated. The change of blade geometry was realized by the free-form deformation (FFD) approach, which was more flexible than traditional parametric methods. A coupled iterative loop was used in a multi-objective optimization process considering two operating conditions. Not only the effect of a single parameter, but also the coupled effects of any two of them were studied. From the Design of Experiment (DoE) results, it was found that the twist and sweep have a relatively strong influence on aerodynamic performance compared with the lean. In addition, it's noteworthy that the effect of twist varied at different operating conditions. At a relatively low mass flow rate, an excessive twist caused a sudden drop in the total pressure ratio. Optimization results showed that the maximum blade stress was dominated by the twist, and a backward sweep at mid-span decreased the stress on the blade surface. The design of twist (DoT) and sweep (DoS) provided a significant improvement of total pressure ratio ranging from 5% to 15% approximately throughout the operating range. Although the peak efficiency was increased by about 1.3% for DoT, the strong tip leakage vortex caused a premature rotating instability compared with the baseline design.

A New Approach to Free-form Cluster Lens Modeling Inspired by the JPEG Image Compression Method

This paper proposes a new approach to free-form cluster lens modeling that is inspired by the JPEG image compression method. This approach is motivated specifically by the need for accurate modeling of high-magnification regions in galaxy clusters. Existing modeling methods may struggle in these regions due to their limited flexibility in the parameterization of the lens, even for a wide variety of free-form methods. This limitation especially hinders the characterization of faint galaxies at high redshifts, which have important implications for the formation of the first galaxies and even for the nature of dark matter. JPEG images are extremely accurate representations of their original, uncompressed counterparts but use only a fraction of number of parameters to represent that information. Its relevance is immediately obvious to cluster lens modeling. Using this technique, it is possible to construct flexible models that are capable of accurately reproducing the true mass distribution using only a small number of free parameters. Transferring this well-proven technology to cluster lens modeling, I demonstrate that this “JPEG parameterization” is indeed flexible enough to accurately approximate an N-body simulated cluster.

A Study on the Fabrication of 3D Scaffolds Using the Solid Freeform Method

A Study on the Fabrication of 3D Scaffolds Using the Solid Freeform Method

The formation of quality and antioxidant properties of bakery products with cloudberry powder

This article discusses the possibility of using the powder from scrap cloudberry in the recipe of bakery products from wheat flour. Bakery products produced using traditional technology and using the freezing baking technology.The powder obtained by drying and chopping cloudberry scrap collected in the Leningrad region. The main recipe used a bakery recipe with 5% sugar and 4% vegetable oil, which replaced flour powder from scrap cloudberry in an amount of 1 to 7%. It was established that the recipe for bakery products made of wheat flour contain 5% of cloudberry powder using the free-form method. In the process of firing intensification of fermentation occurs, which leads to an increase in the acidity of bakery products above the permissible values. The tested high-availability semi-finished products were frozen at minus 18 ° C and stored under these conditions for 2 weeks. Corn powder contributed to better preservation of a specific volume of bakery products. In the ice cream and bakery powder, the antioxidant activity was determined by the FRAP method with orthophenanthroline, titration of tannin with potassium permanganate in the presence of indigocarmine. The use of cloudberry powder increases the antioxidant activity of bakery products, which is facilitated by the hydrolysis of ellaglutanin, during the freezing of test semi-finished products and baking. Compared with products of traditional recipes, baked goods with powder from cloudberry bugs increased antioxidant activity by 1.17 and 1.36 times with simultaneous increase in tannin by 9.8 and 13.7%, respectively, for traditional technology and freezing baking technology.

Integrated free‐form method for aerostructural optimization of wind turbine blades

AbstractA typical approach to optimize wind turbine blades separates the airfoil shape design from the blade planform design. This approach is sequential, where the airfoils along the blade span are preselected or optimized and then held constant during the blade planform optimization. In contrast, integrated blade design optimizes the airfoils and the blade planform concurrently and thereby has the potential to reduce cost of energy (COE) more than sequential design. Nevertheless, sequential design is commonly performed because of the ease of precomputation, or the ability to compute the airfoil analyses prior to the blade optimization. This research compares 2 integrated blade design approaches. The precomputational method combines precomputation with the ability to change the airfoil shapes in limited ways during the optimization. The free‐form method allows for a complete range of airfoil shapes, but without precomputation. The airfoils are analyzed with a panel method (XFOIL) and a Reynolds‐averaged Navier‐Stokes computational fluid dynamics method (RANS CFD). Optimizing the NREL 5‐MW reference turbine showed COE reductions of 2.0%, 4.2%, and 4.7% when using XFOIL and 2.7%, 6.0%, and 6.7% when using RANS CFD for the sequential, precomputational, and free‐form methods, respectively. The precomputational method captures most of the benefits of integrated design for minimal additional computational cost and complexity, but the free‐form method provides modest additional benefits if the extra effort is made in computational cost and development time.

Fiducial-Aided Robust Positioning of Optical Freeform Surfaces.

Form characterization of a machined optical freeform surface demands accurate alignment of the sampled measured data points on the machined surface, and they are compared with the designed geometry of the surface through positioning. In this paper, a fiducial-aided robust positioning method (FAPM) is developed which attempts to evaluate freeform surfaces with high efficiency and precision. The FAPM method makes use of fiducials as reference datum to form a fiducial-aided computer-aided design (FA-CAD) of the freeform surface which not only establishes an inherent surface feature, but also links the different coordinate systems among design coordinate frame, machine tool, and measurement instrument. To verify the capability of the proposed method, a series of experiments were conducted. Compared with the traditional freeform measurement method (e.g., least squares method), the results indicate that the robustness and accuracy of the measurement is significantly enhanced by the FAPM.

结合面型和视场优化策略的自由曲面设计方法

结合面型和视场优化策略的自由曲面设计方法

Free-form surface design method for nonaxial-symmetrical reflectors producing arbitrary image patterns

A free-form (FF) surface design method is proposed for a nonaxial-symmetrical projector system comprising an FF reflector and a light source. The profile of the reflector is designed using a nonaxial-symmetrical FF (NFF) surface construction method such that each incident ray is directed in such a way as to form a user-specified image pattern on the target region of the image plane. The light ray paths within the projection system are analyzed using an exact analytical model and a skew-ray tracing approach. The validity of the proposed NFF design method is demonstrated by means of ZEMAX simulations. It is shown that the image pattern formed on the target region of the image plane is in good agreement with that specified by the user. The NFF method is mathematically straightforward and easily implemented in computer code. As such, it provides a useful tool for the design and analysis stages of optical systems design.

Characterization of New PEEK/HA Composites with 3D HA Network Fabricated by Extrusion Freeforming.

Addition of bioactive materials such as calcium phosphates or Bioglass, and incorporation of porosity into polyetheretherketone (PEEK) has been identified as an effective approach to improve bone-implant interfaces and osseointegration of PEEK-based devices. In this paper, a novel production technique based on the extrusion freeforming method is proposed that yields a bioactive PEEK/hydroxyapatite (PEEK/HA) composite with a unique configuration in which the bioactive phase (i.e., HA) distribution is computer-controlled within a PEEK matrix. The 100% interconnectivity of the HA network in the biocomposite confers an advantage over alternative forms of other microstructural configurations. Moreover, the technique can be employed to produce porous PEEK structures with controlled pore size and distribution, facilitating greater cellular infiltration and biological integration of PEEK composites within patient tissue. The results of unconfined, uniaxial compressive tests on these new PEEK/HA biocomposites with 40% HA under both static and cyclic mode were promising, showing the composites possess yield and compressive strength within the range of human cortical bone suitable for load bearing applications. In addition, preliminary evidence supporting initial biological safety of the new technique developed is demonstrated in this paper. Sufficient cell attachment, sustained viability in contact with the sample over a seven-day period, evidence of cell bridging and matrix deposition all confirmed excellent biocompatibility.