Spatial attitude optimisation of three-dimensional cold mass support system for superconducting magnets for vehicular transport environments

The spatial attitude and dynamic performance of the cold mass support system for superconducting magnets are critical for engineering applications. This study aims to develop a design method for the spatial attitude of tie rods through a series of theoretical derivations and simulations, enabling superconducting magnets to possess a certain degree of dynamic environmental adaptability. This paper first constructs a mathematical model of the three-dimensional cold mass support system under impact loads. Stress formulas for the tie rod under vertical 5<i>g</i>, axial 3<i>g,</i> and lateral 3<i>g</i> impact loads are derived. Based on this, a penalty term for stress differences is introduced to construct the objective function, and the spatial inclination angle of the tie rod is optimised. After determining the acute angle between the tie rod and the coordinate axis, the cold mass support structure exhibits four different attitudes. In order to keep the natural frequency of the magnet away from the main excitation frequency band of vehicle transportation, this study uses the finite element method to perform modal analysis and proposes a method for posture design based on the principle of maximising the first-order natural frequency. Finally, random vibration simulations are conducted for the vibration environment of highway transportation. Reference points are established at both ends of the axis of the magnet body components and the room-temperature tube axis. The displacement response power spectral density (PSD) curves and root mean square values of the reference points during vibration are analysed. The conclusions of this study are as follows. 1) When the acute angles <i>α</i>, <i>β</i>, and <i>γ</i> included between the tie rod and the vertical, axial, and lateral directions are 31.22°, 68.50°, and 68.50°, respectively, the mechanical performance of the three-dimensional cold mass support system reaches its optimal state. 2) When the tie rod is installed in the spatial attitude configuration, the first-order natural frequency of the cold mass system is the highest, with a value of 125.99 Hz. 3) During long-distance integrated vehicle transportation, the maximum values of the vertical and lateral displacements of the magnet assembly axis relative to the room-temperature tube axis are both less than 0.1 mm. The maximum stress locations are both at the root of the carbon fibre tie rod, far below the strength limit of carbon fibre composite materials, indicating that the superconducting magnet possesses a certain degree of dynamic environmental adaptability. These analysis results provide theoretical guidance and data support for the structural safety and stability of this type of superconducting magnet during long-distance integrated vehicle transportation.