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Abstract PurposeTo develop a small‐tip multidimensional RF pulse design procedure that incorporates linear time‐invariant gradient imperfections and concomitant field effects. This could be particularly important for contemporary low‐field MRI systems with high‐performance gradients. Theory and MethodsWe developed an extension of the small‐tip excitation k‐space formalism, where concomitant fields were approximated as a Bloch‐Siegert shift in the rotating frame. This was evaluated using realistic simulations of 2D selective excitation at various field strengths (0.2T, 0.55T, 1.5T, 3T, and 7T) with single and parallel transmit. Simulated excitation profiles from the original and extended k‐space formalisms were compared. Experimental validations were performed at 0.55T with a single‐channel transmit. ResultsThe extended formalism provides improved 2D excitation profiles in all scenarios simulated, compared against the original formalism. The proposed method corrects the concomitant field effects on 2D selective excitations forB0 > 0.2T when the magnitude of theB0is far larger than that of nonrotating concomitant fields. Simulation and phantom experiments at 0.55T match well for both original and proposed methods, with the proposed method providing sharper and more accurate excitation profiles at off‐isocenter distances up to 15 cm. The impact of the proposed method is greatest in scenarios where concomitant fields are substantial, such as low field strengths and off‐isocenter. ConclusionConcomitant fields can be modeled as a Bloch‐Siegert shift in the rotating frame during multidimensional RF pulse design, resulting in improved excitation profiles with sharp edges. This is important to consider for off‐isocenter excitations and imaging at low field strengths with strong gradients.
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This content will become publicly available on February 1, 2026
Reshaping Load-Dependent Mesh Excitation Waveforms of Spur Gears—An Analytical Framework on Tip Relief Modeling and Design
Tip relief is a critical design feature of modern spur gears, aimed at improving dynamic performance through a typical design strategy involving peak-to-peak minimization of mesh excitations. However, due to the hyperstatic nature of simultaneous tooth engagements, the applied torque not only affects mesh deformation amplitudes as normally considered but also alters mesh excitation waveforms, leaving great challenges for the typical design to meet various operating conditions. This paper develops an analytical framework to reshape mesh excitation waveforms, aimed at flexibly reducing vibration intensities across different operating loads and speeds. The load-dependency of excitation harmonics with tip relief is efficiently characterized by an improved analytical mesh excitation model. A tip relief design method is proposed, which automatically recombines harmonic contents of mesh excitations to adapt target operating speeds. Comparisons with finite element models and experiments confirmed the accuracies of quasi-static and dynamic analyses. Parametric studies and application examples further demonstrate the acceptable feasibility and effectiveness of the present method.
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- Award ID(s):
- 2329791
- PAR ID:
- 10600450
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Machines
- Volume:
- 13
- Issue:
- 2
- ISSN:
- 2075-1702
- Page Range / eLocation ID:
- 161
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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