title: Design optimization of MR-compatible rotating anode x-ray tubes for stable operation.
abstract: OBJECTIVE
  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(5)-5 × 10(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(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(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(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.
authors: Department of Radiology, Stanford University, Stanford, California 94305 and Department of Mechanical Engineering, Stanford University, Stanford, California 94305.
authors: Mihye
authors: M
authors: Shin
authors: Prasheel
authors: P
authors: Lillaney
authors: Waldo
authors: W
authors: Hinshaw
authors: Rebecca
authors: R
authors: Fahrig
mesh_terms: D000054:Acceleration; D000465:Algorithms; D004566:Electrodes; D004867:Equipment Design; D020342:Finite Element Analysis; D005471:Fluoroscopy / Q000295:instrumentation; D006358:Hot Temperature; D006801:Humans; D021621:Imaging, Three-Dimensional; D008279:Magnetic Resonance Imaging / Q000295:instrumentation* / Q000379:methods*; D012399:Rotation; D013314:Stress, Mechanical; D019415:Torque; D014732:Vibration; D014965:X-Rays