Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with incre...Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with increasing <em>B</em><sub>0</sub> magnetic field strength. Active shimming is used to generate corrective magnetic fields, which can be used to improve <em>B</em><sub>0</sub> field homogeneity. FASTMAP is an effective shimming technique for computing optimal coil currents, which uses data from six projection directions (or columns): this technique is routinely used for shimming cubic volumes of interest (VOIs). In this paper, we propose several improvements to FASTMAP at 4T. For each shim coil, using a modified 3D gradient-echo pulse sequence, we compute <em>B</em><sub>0</sub> inhomogeneity maps and project them onto eight 1<sup>st</sup> and 2<sup>nd</sup> order spherical harmonic functions. This process is repeated for shim currents between -15,000 to 15,000 with increments of 5000 Digital to Analog Converter (DAC) units, and is used to compute the gradient between spherical harmonic coefficients and DAC values for all 8 shim coils—along with the R<sup>2</sup> values of linear fits. A method is proposed (based on R<sup>2</sup> values) to further refine optimal shim currents in respective coils. We present an analysis that is numerically robust and completely flexible in the selection of the VOIs for shimming. Performance analyses, phantom results, and <em>in vivo</em> results of a human brain are presented, comparing our methods with the FASTMAP method.展开更多
The influence of varying shim layers on the progressive damage/failure of a composite component in a bolted composite-aluminum aerospace structural assembly was investigated using a non-linear three-dimensional(3 D)st...The influence of varying shim layers on the progressive damage/failure of a composite component in a bolted composite-aluminum aerospace structural assembly was investigated using a non-linear three-dimensional(3 D)structural solid elements assembled model of a carbon fiber-reinforced polymer(CFRP)-aluminum single-lap joint with a titanium(Ti-6 Al-4 V)fastener and a washer generated with the commercial finite element(FE)software package,ABAQUS/Standard.A progressive failure algorithm written in Fortran code with a set of appropriate degradation rules was incorporated as a user subroutine in ABAQUS to simulate the non-linear damage behavior of the composite component in the composite-aluminum bolted aerospace structure.The assembled 3 DFE model simulated,as well as the specimen for the experimental testing consisted of a carbon-epoxy IMS-977-2 substrate,aluminum alloy 7075-T651 substrate,liquid shim(Hysol EA 9394),solid peelable fiberglass shim,a titanium fastener,and a washer.In distinction to previous investigations,the influence of shim layers(liquid shim and solid peelable fiberglass shim)inserted in-between the faying surfaces(CFRP and aluminum alloy substrates)were investigated by both numerical simulations and experimental work.The simulated model and test specimens conformed to the standard test configurations for both civil and military standards.The numerical simulations correlated well with the experimental results and it has been found that:(1)The shimming procedure as agreed upon by the aerospace industry for the resolution of assembly gaps in bolted joints for composite materials is the same for a composite-aluminum structure;liquid shim series(0.3,0.5 and 0.7 mm thicknesses)prolonged the service life of the composite component whereas a solid peelable fiberglass shim most definitely had a better influence on the 0.9 assembly gap compared with the liquid shim;(2)The shim layers considerably influenced the structural strength of the composite component by delaying its ultimate failure thereby increasing its service life;and(3)Increasing the shim layer′s thickness led to a significant corresponding effect on the stiffness but with minimal effect on the ultimate load.展开更多
For a superconducting magnet of magnetic resonance imaging （MRI）, the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identifi...For a superconducting magnet of magnetic resonance imaging （MRI）, the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylin- drical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.展开更多
This paper presents an approach of active ferromagnetic shimming for C-type permanent magnetic resonance imaging （MRI） magnet. It is designed to reduce inhomogeneity of magnetostatic field of C-type permanent magnet...This paper presents an approach of active ferromagnetic shimming for C-type permanent magnetic resonance imaging （MRI） magnet. It is designed to reduce inhomogeneity of magnetostatic field of C-type permanent magnet to meet the stringent requirement for MRI applications. An optimal configuration （locations and thicknesses） of active ferromagnetic pieces is generated through calculation according to the initial field map and the demanded final homo- geneity specifications. This approach uses a minimisation technique which makes the sum of squared magnetic moment minimum to restrict the amount of the active ferromagnetic material used and the maximal thickness of pieces stacked at each hole location in the shimming hoards. Simulation and experimental results verify that the method is valid and efficient.展开更多
Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Theref...Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.展开更多
With advantages of small volume,high field strength,and compact stray field,the Halbach array magnet is of great potential in desktop NMR applications.However,field inhomogeneity poses a main obstacle to its applicati...With advantages of small volume,high field strength,and compact stray field,the Halbach array magnet is of great potential in desktop NMR applications.However,field inhomogeneity poses a main obstacle to its applications.Active shimming is necessary for improving the field homogeneity.An active shim coil design method for cylindrical Halbach magnet based on inverse boundary element method(iBEM)is introduced in this work.Shim coils targeting 1st~3rd and Z4/Z5/Z6 spherical harmonic(SH)terms were designed with constraints of field accuracy,resistance,inductance,and current density.Wire loops and symmetric property influence were discussed to further improve the performance of high-order shim coils.Finally,with the prototype of the shim coils constructed,field pattern and SH transformation proved that the coils designed could fit the target SH distribution,though contamination from low-order components existed in highorder terms.A practical shimming experiment on the Halbach magnet has improved the homogeneity from 40.3 ppm to 3.8 ppm in radius 2.5 mm,height 5 mm cylindrical sample space,verifying the coils'compensation ability.This work provides a flexible inverse coil design method for cylindrical Halbach magnet and discusses the high-order shim coil design and implementation,which is potential in nuclear magnetic resonance applications based on Halbach magnet arrays.展开更多
Superconducting magnetic levitation performance, including levitation force and guidance force, is important for the application of high-temperature super- conducting maglev. Both of them are not only affected by diff...Superconducting magnetic levitation performance, including levitation force and guidance force, is important for the application of high-temperature super- conducting maglev. Both of them are not only affected by different arrays of superconductors and magnets, but also by the thickness of the iron shim between permanent magnets. In order to obtain the best levitation performance, the magnetic field distribution, levitation force, and guidance force of a new type of three magnetic hills of permanent magnet guideway with iron shim of different thicknesses （4, 6, and 8 mm） are discussed in this paper. Simulation analysis and experiment results show that the guideway with iron shim of 8 mm thickness possesses the strongest magnetic field and levitation performance when the suspension gap is larger than 10 mm. However, with the decreasing of suspension gap, the guideway with iron shim of 4 mm thickness possesses the best levitation performance. The phenomena can be attributed to the density distribution of flux and magnetization of iron shim.展开更多
The Central Region Model(CRM)is a compact H^- cyclotron.Because of the intrinsic asymmetry of the magnet,its machining and assembly are very complicated.To guarantee the magnet field distribution,it is necessary to me...The Central Region Model(CRM)is a compact H^- cyclotron.Because of the intrinsic asymmetry of the magnet,its machining and assembly are very complicated.To guarantee the magnet field distribution,it is necessary to measure and shim the magnetic field.This paper presents a study on the design and use of the mapping system based on the Hall Effect and the re-machining of shimming bars after analyzing the magnetic field measurement data to achieve the isochronous field and good vertical focusing frequency.The method to effectively reduce the amplitude of the 1st harmonic by shimming bars ls also introduced.展开更多
文摘Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with increasing <em>B</em><sub>0</sub> magnetic field strength. Active shimming is used to generate corrective magnetic fields, which can be used to improve <em>B</em><sub>0</sub> field homogeneity. FASTMAP is an effective shimming technique for computing optimal coil currents, which uses data from six projection directions (or columns): this technique is routinely used for shimming cubic volumes of interest (VOIs). In this paper, we propose several improvements to FASTMAP at 4T. For each shim coil, using a modified 3D gradient-echo pulse sequence, we compute <em>B</em><sub>0</sub> inhomogeneity maps and project them onto eight 1<sup>st</sup> and 2<sup>nd</sup> order spherical harmonic functions. This process is repeated for shim currents between -15,000 to 15,000 with increments of 5000 Digital to Analog Converter (DAC) units, and is used to compute the gradient between spherical harmonic coefficients and DAC values for all 8 shim coils—along with the R<sup>2</sup> values of linear fits. A method is proposed (based on R<sup>2</sup> values) to further refine optimal shim currents in respective coils. We present an analysis that is numerically robust and completely flexible in the selection of the VOIs for shimming. Performance analyses, phantom results, and <em>in vivo</em> results of a human brain are presented, comparing our methods with the FASTMAP method.
基金the Innovation Foundation of National Research Center for Commercial Aircraft Manufacturing Engineering Technology in China (No. SAMC13-JS-13-021)Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology for the provision of financial support
文摘The influence of varying shim layers on the progressive damage/failure of a composite component in a bolted composite-aluminum aerospace structural assembly was investigated using a non-linear three-dimensional(3 D)structural solid elements assembled model of a carbon fiber-reinforced polymer(CFRP)-aluminum single-lap joint with a titanium(Ti-6 Al-4 V)fastener and a washer generated with the commercial finite element(FE)software package,ABAQUS/Standard.A progressive failure algorithm written in Fortran code with a set of appropriate degradation rules was incorporated as a user subroutine in ABAQUS to simulate the non-linear damage behavior of the composite component in the composite-aluminum bolted aerospace structure.The assembled 3 DFE model simulated,as well as the specimen for the experimental testing consisted of a carbon-epoxy IMS-977-2 substrate,aluminum alloy 7075-T651 substrate,liquid shim(Hysol EA 9394),solid peelable fiberglass shim,a titanium fastener,and a washer.In distinction to previous investigations,the influence of shim layers(liquid shim and solid peelable fiberglass shim)inserted in-between the faying surfaces(CFRP and aluminum alloy substrates)were investigated by both numerical simulations and experimental work.The simulated model and test specimens conformed to the standard test configurations for both civil and military standards.The numerical simulations correlated well with the experimental results and it has been found that:(1)The shimming procedure as agreed upon by the aerospace industry for the resolution of assembly gaps in bolted joints for composite materials is the same for a composite-aluminum structure;liquid shim series(0.3,0.5 and 0.7 mm thicknesses)prolonged the service life of the composite component whereas a solid peelable fiberglass shim most definitely had a better influence on the 0.9 assembly gap compared with the liquid shim;(2)The shim layers considerably influenced the structural strength of the composite component by delaying its ultimate failure thereby increasing its service life;and(3)Increasing the shim layer′s thickness led to a significant corresponding effect on the stiffness but with minimal effect on the ultimate load.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60871001)
文摘For a superconducting magnet of magnetic resonance imaging （MRI）, the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylin- drical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.
基金supported by the National Natural Science Foundation of China (Grant No. 60871001)
文摘This paper presents an approach of active ferromagnetic shimming for C-type permanent magnetic resonance imaging （MRI） magnet. It is designed to reduce inhomogeneity of magnetostatic field of C-type permanent magnet to meet the stringent requirement for MRI applications. An optimal configuration （locations and thicknesses） of active ferromagnetic pieces is generated through calculation according to the initial field map and the demanded final homo- geneity specifications. This approach uses a minimisation technique which makes the sum of squared magnetic moment minimum to restrict the amount of the active ferromagnetic material used and the maximal thickness of pieces stacked at each hole location in the shimming hoards. Simulation and experimental results verify that the method is valid and efficient.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2014CB541602)the National Natural Science Foundation of China(Grant Nos.51677008 and 51707028)the Fundamental Research Funds of Central Universities,China(Grant No.106112015CDJXY150003)
文摘Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.
基金Chinese Academy of Sciences MRI Technology Alliance under Grant 2020GZ1004partly by Natural Science Foundation of Shandong Province under Grant ZR2021QA091+1 种基金partly by the Major Innovative Research Team of Suzhou under Grant ZXT2019007partly by the Natural Science Foundation of Tianjin under Grant 17JCYBJC43400.
文摘With advantages of small volume,high field strength,and compact stray field,the Halbach array magnet is of great potential in desktop NMR applications.However,field inhomogeneity poses a main obstacle to its applications.Active shimming is necessary for improving the field homogeneity.An active shim coil design method for cylindrical Halbach magnet based on inverse boundary element method(iBEM)is introduced in this work.Shim coils targeting 1st~3rd and Z4/Z5/Z6 spherical harmonic(SH)terms were designed with constraints of field accuracy,resistance,inductance,and current density.Wire loops and symmetric property influence were discussed to further improve the performance of high-order shim coils.Finally,with the prototype of the shim coils constructed,field pattern and SH transformation proved that the coils designed could fit the target SH distribution,though contamination from low-order components existed in highorder terms.A practical shimming experiment on the Halbach magnet has improved the homogeneity from 40.3 ppm to 3.8 ppm in radius 2.5 mm,height 5 mm cylindrical sample space,verifying the coils'compensation ability.This work provides a flexible inverse coil design method for cylindrical Halbach magnet and discusses the high-order shim coil design and implementation,which is potential in nuclear magnetic resonance applications based on Halbach magnet arrays.
基金supported by the National Magnetic Confinement Fusion Science Program (2011GB112001)the Program of International S&T Cooperation (S2013ZR0595)+2 种基金the National Natural Science Foundation of China (No. 51271155)the Fundamental Research Funds for the Central Universities (SWJTU11CX073, SWJTU11ZT16 and SWJTU11ZT31)the Science Foundation of Sichuan Province (2011JY0031 and 2011JY0130)
文摘Superconducting magnetic levitation performance, including levitation force and guidance force, is important for the application of high-temperature super- conducting maglev. Both of them are not only affected by different arrays of superconductors and magnets, but also by the thickness of the iron shim between permanent magnets. In order to obtain the best levitation performance, the magnetic field distribution, levitation force, and guidance force of a new type of three magnetic hills of permanent magnet guideway with iron shim of different thicknesses （4, 6, and 8 mm） are discussed in this paper. Simulation analysis and experiment results show that the guideway with iron shim of 8 mm thickness possesses the strongest magnetic field and levitation performance when the suspension gap is larger than 10 mm. However, with the decreasing of suspension gap, the guideway with iron shim of 4 mm thickness possesses the best levitation performance. The phenomena can be attributed to the density distribution of flux and magnetization of iron shim.
文摘The Central Region Model(CRM)is a compact H^- cyclotron.Because of the intrinsic asymmetry of the magnet,its machining and assembly are very complicated.To guarantee the magnet field distribution,it is necessary to measure and shim the magnetic field.This paper presents a study on the design and use of the mapping system based on the Hall Effect and the re-machining of shimming bars after analyzing the magnetic field measurement data to achieve the isochronous field and good vertical focusing frequency.The method to effectively reduce the amplitude of the 1st harmonic by shimming bars ls also introduced.
