Geometric Sensitivity Research Articles

Process-induced geometric defect sensitivity of Ti–6Al–4V lattice structures with different mesoscopic topologies fabricated by electron beam melting

Ti–6Al–4V lattice structures with different cell configurations are fabricated by electron beam melting (EBM) method. Two different cell topologies (octet truss and regular rhombic dodecahedron lattice) corresponding to stretching-dominated and bending-dominated respectively are taken into consideration. The mechanical properties of these specimens are examined by quasi-static compression experiments which are conducted by electronic universal machine, while the deformation evolutions of all the specimens are captured by a digital camera. The results indicate that the specimens with rhombic dodecahedron cells exhibit higher specific strength than the octet truss structures. This unusual phenomenon is proved to be caused by the geometric imperfections in the printed stretching-dominated structures. Then the X-ray computed tomography is adopted to capture the process-induced defects in the EBM-printed specimens, and virtual tests are performed by the X-ray tomography based 3D reconstruction model. The computational study explains that the collapse strength of the rhombic dodecahedron (RD) lattice is mainly affected by the surface roughness of the struts, while the weak connection at the joints of the struts leads to the significant reduction in the strength of the octet truss specimens. Meanwhile, the dynamic performance of the printed specimens is predicted by ideal shock wave model and validated by numerical simulation. The results indicate that the defects lead to the significant discrepancy between the theoretical prediction and numerical simulation of octet truss structure, but the failure mode transition of RD lattice structure can be well predicted by the analytical model.

Numerical design and optimization of mechanical vane-type vortex generators in a serpentine air inlet duct

The aim of this work is to investigate the design parameters and optimize the section profile of mechanical vane-type VGs in a sample serpentine air inlet duct by a validated computational model. The design parameters are the height, length, angle of attack and axial location of vortex generators. Total pressure loss (PLC), distortion coefficients (DC(60) and ΔPC/P) and swirl parameters (SC(60) and SI) are assessed in the duct aerodynamic interface plane (AIP) by using twelve layouts of straight vane-type VGs. The geometrical sensitivity analysis of the duct with straight VGs is performed by discrete adjoint formulation. The results of sensitivity analysis indicate that the critical regions of geometry are the leading and trailing edges of VG vanes. By changing straight profile into S-shape type, new VGs are investigated in eight layouts by applying the aforementioned parameters. S-type VGs improve the flow control performance in comparison with the straight ones. The optimal design points are chosen by two different methods with the goal of minimizing the flow loss metrics. Results indicate that all of the optimal design points have the S-type profile and they achieve over 70%, 40% and 20% reductions in distortion, swirl and total pressure loss coefficients at AIP plane, respectively.

Geometric Error Modeling and Sensitivity Analysis of CNC Internal Circular Compound Grinding Machine

In order to improve the machining accuracy and efficiency of the hole and sleeve parts, it is necessary to improve the overall grinding accuracy of the CNC (Computer Numerical Control) internal cylindrical compound grinding machine more accurately and efficiently. First of all, it is necessary to clarify the degree of influence of each error parameter on the grinding accuracy, and compensate each error according to the different degree of influence. In this paper, modeling calculation analysis is carried out for a certain type of CNC internal cylindrical compound grinding machine. Firstly, based on the theory of multi-body system dynamics, the topological structure of the CNC internal cylindrical compound grinder is established. According to the topological structure, the position, motion matrix and error matrix of the moving parts of the grinder are written. After data processing, the numerical control internal cylindrical compound grinder is calculated. Use this model to derivate each error parameter to obtain the sensitivity expression of each error parameter. After the actual structure parameters of the grinder are brought into the expression, the sensitivity coefficient of each error parameter can be determined by normalization treatment. The key error parameter with larger sensitivity coefficient is the key error parameter. Finally, several error parameters which have the greatest impact on the overall grinding accuracy of the grinder are obtained. This method provides the basis for the improvement of the grinding accuracy of the subsequent grinder, and creates conditions for the improvement of the machining accuracy of sleeve parts.

Large-eddy simulation study of unsteady wake dynamics and geometric sensitivity on a skewed bump

Large-eddy simulations of a skewed bump are performed with the bump at angles of and with respect to the free stream. The wake has a large separation bubble and unsteady vortex structures that are highly sensitive to the bump angle. The bump has secondary separation with forward-facing flow in the main separation bubble. The Reynolds stress suggests large-scale motions in the wake, but are insufficient to understand the shedding dynamics. The quasi-periodic shedding cycle is reconstructed using spectral proper orthogonal decomposition. For the case, opposite-sign streamwise vortices are alternately advected downstream in the wake, but only a single vortex is distinguishable in the case. The wake streamwise velocity pulses twice each cycle in the bump, but once per cycle in the bump. The separation bubble and wake oscillate in the spanwise direction. Conditional averaging shows that the vortices are associated with low streamwise velocity and high turbulence. Surface pressures on the bump have negatively skewed distributions in regions on the upstream face and in the separation bubble. In the separation bubble, fluctuations associated with the shedding cycle contribute to the negative skewness.

Cryogenic Cavitation Mitigation in a Liquid Turbine Expander of an Air-Separation Unit through Collaborative Fine-Tuned Optimization of Impeller and Fairing Cone Geometries

An air-separation unit (ASU) uses atmospheric air to produce essential pure gaseous and liquid products for many industrial sectors but requires intensive power consumption. In recent years, cryogenic liquid turbine expanders have been used to replace the traditional J-T valves in air-separation units to save energy. In this paper, an effective design optimization method is proposed to suppress swirling flow and mitigate cavitation in liquid turbines. A flexible tuning of the impeller and fairing cone geometries is simultaneously realized, where the optimization variables are identified via a geometric sensitivity study. A novel objective function is deliberately established by allowing both swirling flow and cavitation characteristics, driving the optimizer to search for deswirling and cavitation-resistant geometries. A kriging surrogate model with an adaptive sampling strategy and a cooperative co-evolution algorithm (CCEA) are incorporated to solve the highly nonlinear optimization problem, where the former reduced the costly evaluations but simultaneously maintained the model prediction accuracy and enabled the aim-oriented global searching (the latter decomposes the problem into several readily solved sub-problems that could be solved in parallel at a high-convergence rate). The optimized impeller and fairing cone geometries were quite favorable for suppressing swirling flow and mitigating cavitation. The impeller cavitation was significantly reduced, with the maximal vapor volume fraction reduced from 0.365 to 0.17 at the blade surface; the diffuser tube high-swirl flow was significantly deswirled and the intensive vapor fraction around the centerline largely reduced, with the maximal vapor volume fraction in the diffuser tube reduced from 0.387 to 0.121. As a result, the isentropic efficiency of the liquid turbine expander was improved from 88.4% to 91.43%.

Patient and scanner-specific variable acquisition times for whole-body PET/CT imaging

Image quality in positron emission tomography (PET) is limited by the number of detected photons. Heavier patients present higher photon attenuation levels, thus increasing image noise. In this work, we propose a new method that uses the combined patient attenuation/system matrix together with a tracer uptake prediction model to optimize scan times for different bed positions in whole body scans. Our main goal is to achieve consistent noise levels across patients and anatomical regions. We propose to optimize scan times for individual bed positions, for patients of any size, based on the scanner sensitivity and patient-specific attenuation. Variable scan times for every bed position were determined by combining the system matrix, derived from the computed tomography (CT) and the scanner-specific geometric sensitivity profiles, and estimations of the global tracer uptake for each patient. The method was validated with anthropomorphic phantoms and whole-body patient 18F-FDG PET/CT scans, where variable and fixed times were compared. Phantom experiments showed that the proposed method was successful in keeping noise level constant for different attenuation setups. In real patients, image noise variability was reduced to less than one-half compared with conventional fixed-time scans at the expense of a four-fold increase in scan times between the biggest and smallest patients. Our method can homogenize image quality not only across patients of different sizes but also across different bed positions of the same patient.

Geometric error contribution modeling and sensitivity evaluating for each axis of five-axis machine tools based on POE theory and transforming differential changes between coordinate frames

The influences of different axes on the accuracy of a machine tool vary due to their positions in the structure of the machine tool and their local errors. In this paper, geometric error contribution modeling and a sensitivity evaluation of the axes of a machine tool are proposed to obtain the influences of each axis and determine the crucial axes of the machine tool. First, the error vector components of the position-independent errors are obtained by product of exponential (POE) theory. Second, the error contributions of all axes are established based on transforming differential changes between coordinate frames by using the POE formula of the tool relative to each axis and the error vectors of the axes. Third, an error sensitivity matrix of each axis is established according to the formula of error contribution about the error vector of the axis. Fourth, two methods are proposed for an error sensitivity evaluation of the axes to determine the crucial axes: one method employs the weights of the error contributions of the axes, and the other method employs the error sensitivity coefficients of the axes. Finally, simulations and real cutting experiments are carried out with the SmartCNC500_DRTD five-axis machine tool to verify the effectiveness of the error contribution modeling and error sensitivity evaluation of the axis.

Calculating the k-Eigenvalue Sensitivity to Typical Geometric Perturbations with the Adjoint-Weighted Method in the Continuous-Energy Reactor Monte Carlo Code RMC

Geometric sensitivity analyses of the -eigenvalue have many applications in analyses of geometric uncertainty, calculations of differential control rod worth, and searches for critical geometry. The adjoint-weighted first-order geometric sensitivity theory is widely used and has continuously evolved with the Monte Carlo methods. However, the existing adjoint-weighted algorithm can do only uniform isotropic expansions or contractions of surfaces. The adjoint-weighted algorithm also requires computation of adjoint-weighted scattering and fission reaction rates exactly at material interfaces, which has an infinitesimal probability in reality. This paper presents an improved geometry adjoint-weighted perturbation algorithm that is incorporated into the continuous-energy Reactor Monte Carlo (RMC) code. The improvement of the adjoint-weighted algorithm is decomposed into three steps for constructing a cross-section function of geometric parameters using logical expressions, calculating the derivative of the cross-section function, and estimating the adjoint-weighted surface reaction rates. The improved algorithm can accommodate common one-parameter geometric perturbations of internal interfaces or boundary surfaces as well as those of cells as long as the perturbed cells can be described by logical expressions of spatial surface equations. The perturbation algorithm is compared with a direct difference method, the linear least-squares fitting method with central differences, for several typical geometric perturbations including translation, fixed-axis rotation, and uniform isotropic/anisotropic expansion transformations of planar, spherical, cylindrical, and conical surfaces. The differences between the two methods are not more than 3% and not more than 3 for the majority of the test examples. Even though the perturbation algorithm has higher figures of merit than the direct difference method for the majority of the test examples, there is no guarantee that the former can always be more efficient than the latter. The limitation in the efficiency of the perturbation algorithm was demonstrated by the totally reflecting light water reactor pin model.

Discrete Adjoint Approach for Nonlinear Unsteady Aeroelastic Design Optimization

Presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities, which can subsequently be used for nonlinear unsteady aeroelastic geometric design optimization. The methodology is applicable to compressible Reynolds-averaged Navier–Stokes computational-fluid-dynamics solvers and is based on a harmonic balance nonlinear frequency-domain technique for modeling nonlinear aerodynamics in the frequency domain. Automatic differentiation is used to derive the computer code representing the adjoint gradient of the harmonic balance computational-fluid-dynamics solver. Discrete adjoint method airfoil geometric design nonlinear unsteady aerodynamic sensitivities are first computed for a benchmark NLR 7301 airfoil transonic aeroelastic configuration, and results are compared with finite difference computations to demonstrate the accuracy of the methodology. The airfoil surface is mathematically curve-fit using an airfoil parameterization technique, and the discrete adjoint methodology provides the gradient of the flutter onset or limit-cycle oscillation reduced velocity with respect to changes in each of the parameters of the airfoil curve-fit methodology for the cost of a single adjoint solution. This gradient information is supplied to a limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization solver, which then determines values for the curve-fit parameters that maximize flutter onset or limit-cycle oscillation reduced velocity. The discrete adjoint nonlinear unsteady aeroelastic geometric design sensitivity computation methodology is then used to redesign the shape of the benchmark NLR 7301 airfoil aeroelastic configuration to optimize the aeroelastic flutter onset reduced velocity or the reduced velocity for a specified limit-cycle oscillation response amplitude.

Geometrical sensitivity analysis based on design optimization and multiphysics analysis of PM assisted synchronous reluctance motor

Geometrical sensitivity analysis based on design optimization and multiphysics analysis of PM assisted synchronous reluctance motor

Geometric Sensitivity of Variable Pinhole SPECT with a Keel-edge Pinhole Model

A variable pinhole (VP) collimator is formed by stacking several tungsten plates with different apertures. The configuration of the VP can be optimized for target region-of-interests at different rotation angles. Hence, both the resolution and sensitivity of the system can be improved. However, it is difficult to analytically implement the exact system model that simulates the step shapes between adjacent layers. In this study, we compared the conventional keel-edge and knife-edge pinhole models with the VP model using simulations. The keel-edge and knife-edge models were evaluated based on various specifications to identify the optimum system model. The simulation results showed that the keel-edge model with 80% channel length (keel-edge 80%) elicits the best performance with a fixed acceptance angle and pinhole plate thickness. The results in this study are expected to be applied to full-scale SPECT with a VP collimator which is currently under development.

SiPM-based PET detector module for a 4π span scanner

Abstract Detectors in Positron Emission Tomography (PET) scanners are usually arranged in rings with the specimen lying along the axial direction. This distribution, however, does not maximize the geometrical sensitivity unless the axial extent becomes much longer than the axial Field of View (FOV), a very costly solution. The optimal geometry for a PET scanner is a sphere with the specimen located at the center. The state of the art of scintillator crystals and detectors for γ -rays does not facilitate smooth spherical geometry design. In this work we propose a PET scanner of 4 π steradian coverage for preclinical imaging as a proof of concept. As a first approximation to the ideal spherical topology, the scanner is shaped as an icosahedron. Furthermore we also present the new custom-tailored hexagonal Silicon Photomultiplier (SiPM) and a monolithic laser-engraved LYSO scintillator crystal that tiles the twenty scanner faces. Preliminary results of the scanner performance based on simulations point to enhanced sensitivity. Initial results on the characterization of the hexagonal photodetector by collection of pulses from a 22Na point source show similar performance as conventional square pixels with the benefit of the increased sensitivity and resolution.

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an over-constrained parallel tracking mechanism. The main contribution is the consideration of over-constrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore, two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.

Synthetic investigation of thermal storage capacities in crystalline bedrock through a regular fracture network as heat exchanger

Crystalline rocks are in general considered of poor interest for geothermal applications at shallow depths (<100 m), in particular because of their low permeability. In some cases, fractures may enhance permeability, but thermal energy storage at these shallow depths still remains challenging because of the complexity of fractured media to efficiently manage water circulation. To assess the feasibility of efficient thermal energy storage in shallow fractured crystalline bedrocks and to determine the fracture network geometric parameters that control heat storage in fractured media, we investigate abilities of a synthetic model especially dedicated to an innovative semi open-loop heat exchanger. The representative heat exchanger system consists of a network of star-shaped grooves radially arranged around a central borehole hydraulically and thermally insulated from the grooves. Fluid is injected in the downward direction into the grooves and withdrawn upward in the central insulated pipe. Heat is exchanged with the rock only through the grooves. The three geometrical parameters controlling the thermal storage are the width, the height and the number of grooves. With a dimensional analysis on heat transport equations and a sensitivity analysis on geometric parameters, we show that the conduction of temperature in rocks presents two well-separated short-term and long-term regimes. At short-term, maximum of exchanges is reached at the beginning of the heated water injection into the grooves. It is controlled by the thermal exchange surface depending on the number and width of the grooves. During the long-term regime, the heat exchanger capacity is mainly controlled by the accessible rock to thermal storage which depends mainly on the width of the grooves. We finally discuss about the possibility of extending the results obtained from the star-shaped geometric sensitivity study to natural fracture systems.

A microfabrication approach for making metallic mechanical metamaterials

A scalable technique for making octet microlattice topology mechanical metamaterials with a cell size of 1 mm or less from thin stainless steel sheets is described. The microfabrication process used a perforation operation to form planar truss sheets by the periodic removal of rectangular shaped material. A simultaneous perforation and corrugation operation was also used to create a single layer of trusses with a pyramidal topology. A 3D lattice was then assembled by alternatively stacking the pyramidal and planar truss sheets, taking care to align their nodes to form the octet lattice truss topology. A vacuum brazing method was used to metallurgically bond the assembly. The compressive properties of the microlattices are shown to be comparable to those of much larger cell-size structures of similar material and topology. An assessment of geometric imperfection sensitivity indicates where further mechanical property improvements could be realized by improving the precision of both the perforation and assembly process.

Investigation of geometric sensitivity of a non-axisymmetric bump: 3D mean velocity measurements

The geometric sensitivity of a non-axisymmetric bump with $$H/\delta =2$$ is studied with 3D magnetic resonance velocimetry (MRV). The geometry is modified by rotating the bump with respect to the flow. 3D MRV is used to study the flow at bump angles of $$0^{\circ }$$ , $$5^{\circ }$$ , $$10^{\circ }$$ , $$40^{\circ }$$ , $$50^{\circ }$$ , and $$60^{\circ }$$ . For the symmetric $$0^{\circ }$$ case, the mean flow shows common-up vortex structures in the near wake but common-down structures in the far wake. Angled cases have one strong vortex structure that exists through the entire wake. The volume of the separation bubble and the vortex structures are sensitive to the bump angle.

Structural behavior of shallow geodesic lattice domes

This paper describes experiments and analysis of the complete post-buckling behavior of shallow geodesic lattice domes. Although individual members are straight, their geometric arrangement approximates a curved surface and typical behavior is highly nonlinear, including the possibility of sudden jumps in which there may be multiple discontinuous pops from one equilibrium configuration to another. A number of shallow domes were produced using a 3D printer and tested using a load cell and proximity laser sensor. In contrast to most previous studies, rather than pinned or semi-rigid joints, the lattices studied here incorporate moment-transmitting joints and clamped boundary conditions at the perimeter. Thus, flexure is the dominant mode of deformation under lateral loading and coupled instability behaviors are possible in practice. The complete load-displacement relationship and multiple equilibrium configurations are exhibited both in experiment and in simulation. The experimental data shows a close correlation with nonlinear finite element analysis using path-following techniques. A typical member (coupled) buckling behavior and its influence on the critical load are presented. Conclusions are drawn with respect to symmetry and geometric sensitivity.

3D non-invasive inspection of the skin lesions by close-range and low-cost photogrammetric techniques

In dermatology, one of the most common causes of skin abnormality is an unusual change in skin lesion structure which may exhibit very subtle physical deformation of its 3D shape. However the geometrical sensitivity of current cost-effective inspection and measurement methods may not be sufficient to detect such small progressive changes in skin lesion structure at micro-scale. Our proposed method could provide a low-cost, non-invasive solution by a compact system solution to overcome these shortcomings by using close-range photogrammetric imaging techniques to build a 3D surface model for a continuous observation of subtle changes in skin lesions and other features.

Continuum shape sensitivity analysis for aeroelastic gust using an arbitrary lagrangian-eulerian reference frame

Continuum Sensitivity Analysis (CSA), a method to determine response derivatives with respect to design variables, is derived here for the first time in an arbitrary Lagrangian-Eulerian (ALE) reference frame. CSA differentiates nonlinear governing system of equations to arrive at a linear system of partial differential continuum sensitivity equations (CSEs), here, for fluid-structure interaction (FSI). The CSEs and associated sensitivity boundary conditions are derived here for the first time for FSI, using the boundary velocity formulation, carefully distinguishing design velocity from flow velocity and ALE mesh velocity. Whereas boundary conditions must be differentiated using the material (total) derivative, it is sometimes advantageous to derive the CSEs using local (partial) derivatives. The benefit is that geometric sensitivity, known as design velocity, may not be required in the domain. It is shown here that this advantage is realized when the ALE frame undergoes only the rigid body motion associated with the structure to which it is attached. It is further shown that the advantage is not realized when the ALE mesh deforms due to the flexible motion of the fluid-structure interface. The equations for the transient gust response of a two-dimensional airfoil in compressible flow, flexibly attached to a rigid body mass, are presented as a model problem to illustrate a detailed derivation.

Effect of morphology on nanoparticle transport and deposition in human upper tracheobronchial airways

Aerosol transport and deposition in human lungs has attracted considerable attention in the past few years, as it has significant value to the study of toxicity consequence as well as therapeutic potential in occupational health and medical applications. In reproducing human tracheobronchial airways, two approaches were frequently taken: (1) anatomical realistic reconstruction through image scans (e.g. CT and MRI) or cadaver casts and (2) mathematical description using simplified models. Strengths and limitations are primarily focused on accuracy, resolution, repeatability, and computational\physical expenses. While both approaches were reported in literature, detailed comparison of aerosol transport and deposition in the two representations were scarcely performed, largely due to the challenge to acquire comprehensive data from the irregular structured airway replicas (approach 1). To fill the gap, the current study performed a numerical comparison of nanoparticle transport and deposition in human upper tracheobronchial airways by using an anatomical realistic reconstruction (through CT scans) and a mathematically simplified airway model. As the first step, the current study was focused on the variation in breathing airflow pattern and the effect towards fate of the inhaled nanoparticles in human upper tracheobronchial airways. The study provided important information to understand geometric sensitivity of nanoparticle modeling in the human tracheobronchial tree and is of significant value to predict the whole lung uptake of inhaled nanoparticles in the human respiratory system.