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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Optimization of ultrasonic array inspections using an efficient hybrid model and real crack shapes

Models which simulate the interaction of ultrasound with cracks can be used to optimize ultrasonic array inspections, but this approach can be time-consuming. To overcome this issue an efficient hybrid model is implemented which includes a finite element method that requires only a single layer of elements around the crack shape. Scattering Matrices are used to capture the scattering behavior of the individual cracks and a discussion on the angular degrees of freedom of elastodynamic scatterers is included. Real crack shapes are obtained from X-ray Computed Tomography images of cracked parts and these shapes are inputted into the hybrid model. The effect of using real crack shapes instead of straight notch shapes is demonstrated. An array optimization methodology which incorporates the hybrid model, an approximate single-scattering relative noise model and the real crack shapes is then described.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

42 ENGINEERING↗
DOE OSTI2018

Numerical Analysis of the Effect of Infrared Radiation on Cryogenic Inertial Confinement Fusion Targets

The present work applies the finite element method to calculate the maximum allowable time that cryogenic inertial confinement fusion (ICF) targets can be exposed to infrared radiation (IR). Hence, a 3-D numerical model integrated with discrete coordinate radiation model was developed to investigate the influence of transmittance of the laser entrance holes (LEHs) and boundary conditions on the temperature field distribution and the maximum DT layer deterioration time for CH, Be, and diamond capsules. Our study shows that introducing such a radiation model can accurately obtain more detailed spatial and temporal distribution information in the ICF targets. The simulation results demonstrate that the Be and diamond capsules provided much better temperature field homogenization than the CH capsule under equivalent boundary conditions, but the CH capsule was heated more by IR radiation than the Be and diamond. In addition, the maximum DT layer deterioration time was significantly increased to 3 s when decreasing the transmittance of the LEH from 0.2 to 0.01. However, either reducing the capsule IR absorption or increasing the inner hohlraum IR absorption demonstrated no conclusive increase in the maximum DT layer deterioration time. These results are expected to provide useful parameters in the design of cryogenic targets and shroud systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Laser-excited optical emission response of CdTe quantum dot/polymer nanocomposite under shock compression

Laser-driven shock compression experiments and corresponding finite element method simulations are carried out to investigate the blueshift in the optical emission spectra under continuous laser excitation of a dilute composite consisting of 0.15% CdTe quantum dots by weight embedded in polyvinyl alcohol polymer. This material is a potential candidate for use as internal stress sensors. The analyses focus on the time histories of the wavelength blue-shift for shock loading with pressures up to 7.3 GPa. The combined measurements and calculations allow a relation between the wavelength blueshift and pressure for the loading conditions to be extracted. It is found that the blueshift first increases with pressure to a maximum and subsequently decreases with pressure. This trend is different from the monotonic increase of blueshift with pressure observed under conditions of quasistatic hydrostatic compression. Additionally, the blueshift in the shock experiments is much smaller than that in hydrostatic experiments at the same pressure levels. The differences in responses are attributed to the different stress states achieved in the shock and hydrostatic experiments and the time dependence of the mechanical response of the polymer in the composite. The findings offer a potential guide for the design and development of materials for internal stress sensors for shock conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Effect of interfacial transition zone on the Young's modulus of carbon nanofiber reinforced cement concrete

Identifying the properties of the region where the cement paste meets the aggregate surface (interfacial transition zone, ITZ) is critical to understanding the strength and fracture behavior of carbon nanofiber (CNF) reinforced cement concrete. In this study, the finite element method is employed to investigate the effect of the ITZ on the Young's modulus of cement concrete made with CNF. The numerical models for cement concrete with and without CNF are constructed based on the digital image processing technique. To consider the interface effect, the concept of ''effective aggregate'' is put forward, namely, the Young's modulus and Poisson's ratio for each aggregate particle are replaced by an effective Young's modulus and effective Poisson's ratio, in which the effect of thickness and the Young's modulus of ITZ is taken into account in an averaged manner. Then, the quantitative nanomechanical mapping (based on atomic force microscopy) technique is adopted to measure the Young's modulus and thickness of ITZ with and without CNFs, which are further used as the input parameters in the numerical model. The numerical simulation results are verified by experimental testing, which indicates that the ITZ effect should be considered when implementing the numerical simulation. In addition, this analysis shows that compared with the plain cement concrete, CNFs can greatly enhance the mechanical properties of ITZ, which will in turn improve the Young's modulus of cement concrete significantly. Finally, the effect of thickness and Young's modulus of ITZ on the Young's modulus of CNF reinforced cement concrete is also discussed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2017

Fast Reactor Core Analysis Using AZNHEX Neutron Diffusion Code

The AZTLAN platform project emerged as an initiative to rank Mexico at a competitive level in software aspects for the analysis of nuclear reactors, in an effort to achieve autonomy in this area. The AZTLAN platform is conformed by a thermo-hydraulic code (AZTHECA), a neutron transport code (AZTRAN) and two neutron diffusion codes (AZKIND, AZNHEX). AZNHEX is a 3D diffusion code that solves numerically the time dependent neutron diffusion equations in hexagonal z-geometry using the RTN0 nodal finite element method. With this code, it is possible to simulate and analyze light water reactors, such as the Russian VVER, and variety of fast reactors. In this work, a sodium-cooled fast reactor core in steady state, with control rods fully withdrawn, is simulated. The comparison and validation of the values obtained with AZNHEX was done with the results obtained with MCNP6 Monte Carlo code.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Validating corrosion models: Influence of physical properties

In chloride containing environments, two metals in physical contact can undergo galvanic corrosion limiting the lifetime of components. Being able to accurately predict galvanic corrosion damage distributions over time has not been widely presented in literature. Therefore, Finite Element Method (FEM) corrosion models were experimentally validated for two galvanic couples as a function of governing equations, environment, anode material, anode:cathode ratio, and time. Carbon steel/stainless steel (CS/SS) and zinc/stainless steel (Zn/SS) galvanic couples were exposed to NaCl solutions at room temperatures for up to 14 days. For the galvanic couples and environments, the Laplace equation with variable conductivity and reactions was sufficient to model the experimental corrosion damage. Increasing the chloride concentration for the CS/SS galvanic couple, regardless of the anode:cathode ratio, decreased the observed and modeled corrosion damage. Decreasing the anode:cathode ratio (i.e., increasing the cathode length), increased the experimentally observed and modeled corrosion damage. For small anode:cathode ratios, the governing equations deviate over long time periods with the Nernst-Plank equation being conservative. For the Zn/SS galvanic couple, the cathode length controls the dominant cathodic reduction reaction. For small cathode lengths, the hydrogen evolution reaction is dominant. For larger cathode lengths, the oxygen reduction reaction is dominant. The results are discussed with regard to the influence of solution chemistry, ohmic drop, and governing reactions. Overall, validated FEM models were presented, and the resultant models, physics, and mechanisms can be applied to other corrosion scenarios with confidence.

Carbon steel↗
DOE OSTI2025

Validating corrosion models: A comparison of governing equations

Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.

Carbon steel↗
DOE OSTI2018

A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data

Here, we present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Following a standard approach with the X-FEM, as the crack propagates into new regions of the domain, elements are split into several copies that contain pieces of the domain on either side of the crack. We examine quadrature rules that have sufficient accuracy to calculate stiffness matrices regardless of the orientation of the crack with respect to the element. This permits the number of integration points within elements to remain constant as a crack propagates, and for state data to be easily transferred between successive discretizations. In order to maintain weights that are strictly positive, we propose an approach that blends moment-fitted weights with volume-fraction based weights. To demonstrate the efficacy of this simple approach, we present results from numerical tests and examples with both elastic and plastic material response.

42 ENGINEERING↗
DOE OSTI2016

U-10Mo/Zr Interface Modeling using a Microstructure-Based FEM Approach

The U-10Mo in low enrichments (LEU) has been identified as the most promising alternative to the current highly enriched uranium (HEU) used in the United States’ fleet of high performance research reactors (USHPRRs). The nominal configuration of the new LEU U-10Mo plate fuel comprises a U-10Mo fuel foil enriched to slightly less than 20% U-235 (0.08” to 0.02” thick), a thin Zr interlayer/diffusion barrier (25 m thick) and a relatively thick outer can of 6061 aluminum. Currently, the Zr interlayer is clad by hot roll bonding. Previous studies and observations revealed a thinning of the zirconium (Zr) layer during this fuel fabrication process, which is not desirable from the fuel performance perspective. Coarse UMo grains, dendritic structures, Mo concentration segregation, carbides, and porosity are present in the as-cast material and can lead to a nonuniform UMo/Zr interface. The purpose of the current work is to investigate the effects of these microstructural parameters on the Zr coating variation. A microstructure-based finite-element method model was used in this work, and a study on the effect of homogenization on the interface between U-10Mo and Zr was conducted. The model uses actual backscattered electron–scanning electron microscopy microstructures, Mo concentrations, and mechanical properties to predict the behavior of a representative volume element under compressive loading during the rolling process. The model successfully predicted the experimentally observed thinning of the Zr layer in the as-cast material. The model also uses results from a homogenization model as an input, and a study on the effect of different levels of homogenization on the interface indicated that homogenization helps decrease this thinning. This model can be considered a predictive tool representing a first step for model integration and an input into a larger fuel fabrication performance model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Simulated effects of sample size and grain neighborhood on the modeling of extreme value fatigue response

Assessing the size of representative volume elements (RVEs) for fatigue-related applications is challenging. A RVE relevant to random microstructure requires a volume of material that is sufficiently large to capture the grain/phase heterogeneity that captures all statistical moments of the distribution of the driving force for fatigue crack formation at “hot spot” grains. Consequently, the large size of a microstructure RVE required to study fatigue phenomena is largely computationally intractable and difficult to explore. A more realistic objective in this work is to systematically study, as a function of the size of a statistical sample of microstructure, trends towards convergence of the simulated distribution of driving force for fatigue crack formation. Our present work accordingly leverages the recently developed open-source PRISMS-Fatigue framework to examine the trends in convergence of extreme value distributions (EVD) of Fatigue Indicator Parameters (FIPs) in progressively larger polycrystalline microstructure realizations of FCC Al alloy 7075-T6 using crystal plasticity finite element method simulations. The results are compared to the traditional method in which ensembles of statistical volume elements (SVEs) are simulated to build up statistics intended to approximate those associated with a larger volume of material. The convergence of EVDs with increase of size of a SVE of microstructure is closely related to the extent of grain nearest neighbor (NN) interactions. Accordingly, the sensitivity of the local micromechanical response at hot spot grains is quantitatively investigated by systematically varying the orientations of NN grains. Results indicate that SVEs with cubic crystallographic texture tend towards convergence of the EVD of FIPs with tens of thousands of grains while the random and rolled textures require larger volumes. Simple relationships based on microstructure parameters (e.g., Schmid Factor, grain size, NN misorientation) do not completely correlate to fatigue hot spot grains. Finally, the sensitivity of the extreme value fatigue response at hot spot grains extends to the 3rd NN when a single neighborhood grain orientation is altered.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Analysis of the transient behavior of rubbing components

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

Quezdou, M. B.↗
DOE OSTI2025

Multi-objective surrogate-assisted calibration of CPFEM models using macroscopic response and in situ EBSD measurements of grain reorientation trajectories

Crystal plasticity finite element method (CPFEM) models are widely used to simulate the deformation behaviour of polycrystalline materials, but their calibration is often limited by their high computational cost and the non-convexity of the optimisation landscape. Here, this study develops a multi-objective surrogate-assisted calibration workflow that couples a multi-objective genetic algorithm (MOGA) with an adaptively trained deep neural network (DNN) surrogate model to efficiently identify CPFEM parameters from experimental data. The workflow is demonstrated on three crystal plasticity (CP) formulations of increasing complexity — Voce hardening (VH), two-coefficient latent hardening (LH2), and six-coefficient latent hardening (LH6) — using in situ electron backscatter diffraction (EBSD) measurements of Alloy 617 under uniaxial tensile loading. The CPFEM models are calibrated against the experimentally observed stress–strain response and reorientation trajectories of eight grains, then validated against eight additional trajectories and overall texture evolution. Across the CP formulations, the macroscopic response was reproduced reliably, while differences emerged in the robustness and accuracy of the grain-scale predictions. Including grain reorientation trajectories in the multi-objective calibration improved texture evolution predictions and filtered out physically inconsistent parameter sets that can arise from calibrating against only the stress–strain data. The workflow also demonstrates good transferability of calibrated parameters from a low- to a high-fidelity microstructural model. These results provide practical guidance for integrating in situ microstructural data into CPFEM through efficient, repeatable, and physically meaningful multi-objective calibration.

Crystal plasticity finite element method↗
DOE OSTI2018

Superconvergence analysis for nonlinear parabolic equation with EQ{sub 1}{sup rot} nonconforming finite element

EQ{sub 1}{sup rot} nonconforming finite element method (FEM) applied to a class of nonlinear parabolic equation is discussed. First, by use of two typical characters of this element (one is that the associated FE interpolation operator is identical to its traditional Ritz projection operator; the other is that the consistency error is of order O(h{sup 2}), one order higher than the interpolation error, when the exact solution of the problems belongs to H{sup 3}(Ω)), the supercloseness of order O(h{sup 2}) in broken H{sup 1}-norm for semi-discrete scheme is obtained without the boundedness of numerical solution in L{sup ∞}-norm through splitting the numerical solution into several parts. Moreover, we get the desired result with requirement of u,u{sub t}∈H{sup 3}(Ω) only. Secondly, a linearized Crank–Nicolson fully discrete scheme is proposed and the superclose property of order O(h{sup 2}+τ{sup 2}) is derived by constructing a suitable auxiliary problem. Finally, a numerical example is carried out to confirm our theoretical analysis. Here, h is the subdivision parameter and τ is the time step.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly set negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

The Effect of Data Transformations on Scalar Field Topological Analysis of High-Order FEM Solutions

High-order finite element methods (HO-FEM) are gaining popularity in the simulation community due to their success in solving complex flow dynamics. There is an increasing need to analyze the data produced as output by these simulations. Simultaneously, topological analysis tools are emerging as powerful methods for investigating simulation data. Yet, most of the current approaches to topological analysis have had limited application to HO-FEM simulation data for two reasons. First, the current topological tools are designed for linear data (polynomial degree one), but the polynomial degree of the data output by these simulations is typically higher (routinely up to polynomial degree six). Second, the simulation data and derived quantities of the simulation data have discontinuities at element boundaries, and these discontinuities do not match the input requirements for the topological tools. One solution to both issues is to transform the high-order data to achieve low-order, continuous inputs for topological analysis. Nevertheless, there has been little work evaluating the possible transformation choices and their downstream effect on the topological analysis. We perform an empirical study to evaluate two commonly used data transformation methodologies along with the recently introduced L-SIAC filter for processing high-order simulation data. Our findings indicate diverse behaviors are possible. We offer some guidance about how best to consider a pipeline of topological analysis of HO-FEM simulations with the currently available implementations of topological analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Impact of the MLC on the MRI field distortion of a prototype MRI-linac

Purpose: To cope with intrafraction tumor motion, integrated MRI-linac systems for real-time image guidance are currently under development. The multileaf collimator (MLC) is a key component in every state-of-the-art radiotherapy treatment system, allowing for accurate field shaping and tumor tracking. This work quantifies the magnetic impact of a widely used MLC on the MRI field homogeneity for such a modality.Methods: The finite element method was employed to model a MRI-linac assembly comprised of a 1.0 T split-bore MRI magnet and the key ferromagnetic components of a Varian Millennium 120 MLC, namely, the leaves and motors. Full 3D magnetic field maps of the system were generated. From these field maps, the peak-to-peak distortion within the MRI imaging volume was evaluated over a 30 cm diameter sphere volume (DSV) around the isocenter and compared to a maximum preshim inhomogeneity of 300 μT. Five parametric studies were performed: (1) The source-to-isocenter distance (SID) was varied from 100 to 200 cm, to span the range of a compact system to that with lower magnetic coupling. (2) The MLC model was changed from leaves only to leaves with motors, to determine the contribution to the total distortion caused by MLC leaves and motors separately. (3) The system was configured in the inline or perpendicular orientation, i.e., the linac treatment beam was oriented parallel or perpendicular to the magnetic field direction. (4) The treatment field size was varied from 0 × 0 to 20×20 cm{sup 2}, to span the range of clinical treatment fields. (5) The coil currents were scaled linearly to produce magnetic field strengths B{sub 0} of 0.5, 1.0, and 1.5 T, to estimate how the MLC impact changes with B{sub 0}.Results: (1) The MLC-induced MRI field distortion fell continuously with increasing SID. (2) MLC leaves and motors were found to contribute to the distortion in approximately equal measure. (3) Due to faster falloff of the fringe field, the field distortion was generally smaller in the perpendicular beam orientation. The peak-to-peak DSV distortion was below 300 μT at SID≥130 cm (perpendicular) and SID≥140 cm (inline) for the 1.0 T design. (4) The simulation of different treatment fields was identified to cause dynamic changes in the field distribution. However, the estimated residual distortion was below 1.2 mm geometric distortion at SID≥120 cm (perpendicular) and SID≥130 cm (inline) for a 10 mT/m frequency-encoding gradient. (5) Due to magnetic saturation of the MLC materials, the field distortion remained constant at B{sub 0}>1.0 T.Conclusions: This work shows that the MRI field distortions caused by the MLC cannot be ignored and must be thoroughly investigated for any MRI-linac system. The numeric distortion values obtained for our 1.0 T magnet may vary for other magnet designs with substantially different fringe fields, however the concept of modest increases in the SID to reduce the distortion to a shimmable level is generally applicable.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Design optimization of MR-compatible rotating anode x-ray tubes for stable operation

Purpose: Hybrid x-ray/MR systems can enhance the diagnosis and treatment of endovascular, cardiac, and neurologic disorders by using the complementary advantages of both modalities for image guidance during interventional procedures. Conventional rotating anode x-ray tubes fail near an MR imaging system, since MR fringe fields create eddy currents in the metal rotor which cause a reduction in the rotation speed of the x-ray tube motor. A new x-ray tube motor prototype has been designed and built to be operated close to a magnet. To ensure the stability and safety of the motor operation, dynamic characteristics must be analyzed to identify possible modes of mechanical failure. In this study a 3D finite element method (FEM) model was developed in order to explore possible modifications, and to optimize the motor design. The FEM provides a valuable tool that permits testing and evaluation using numerical simulation instead of building multiple prototypes.Methods: Two experimental approaches were used to measure resonance characteristics: the first obtained the angular speed curves of the x-ray tube motor employing an angle encoder; the second measured the power spectrum using a spectrum analyzer, in which the large amplitude of peaks indicates large vibrations. An estimate of the bearing stiffness is required to generate an accurate FEM model of motor operation. This stiffness depends on both the bearing geometry and adjacent structures (e.g., the number of balls, clearances, preload, etc.) in an assembly, and is therefore unknown. This parameter was set by matching the FEM results to measurements carried out with the anode attached to the motor, and verified by comparing FEM predictions and measurements with the anode removed. The validated FEM model was then used to sweep through design parameters [bearing stiffness (1×10{sup 5}–5×10{sup 7} N/m), shaft diameter (0.372–0.625 in.), rotor diameter (2.4–2.9 in.), and total length of motor (5.66–7.36 in.)] to increase the fundamental frequency past the operating range at 50 Hz.Results: The first large vibration during the prototype motor operation was obtained at 21.64±0.68 Hz in the power spectrum. An abrupt decrease in acceleration occurred at 21.5 Hz due to struggling against the resonance vibrations. A bearing stiffness of 1.2×10{sup 5} N/m in the FEM simulation was used to obtain a critical speed of 21.4 Hz providing 1.1% error. This bearing stiffness value and the 3D model were then confirmed by the experiments with the anode removed, demonstrating an agreement within 6.4% between simulation results and measurements. A calculated first critical frequency (fundamental frequency) of 68.5 Hz was obtained by increasing the bearing stiffness to 1×10{sup 7} N/m and increasing the shaft diameter by 68.0%. Reducing the number of bearings in the design permits decreasing the total length of the motor by 1.7 in., and results in a fundamental frequency of 68.3 Hz in concert with additional changes (shaft diameter of 0.625 in., rotor diameter of 2.4 in., and bearing stiffness of 1×10{sup 6} N/m).Conclusions: An FEM model of the x-ray tube motor has been implemented and experimentally validated. A fundamental frequency above the operational rotation speed can be achieved through modification of multiple design parameters, which allows the motor to operate stably and safely in the MR environment during the repeated acceleration/deceleration cycles required for an interventional procedure. The validated 3D FEM model can now be used to investigate trade-offs between generated torque, maximum speed, and motor inertia to further optimize motor design.

62 RADIOLOGY AND NUCLEAR MEDICINE↗