Simulation and Optimization of Hemispherical Resonator's Equivalent Bottom Angle for Frequency-Splitting Suppression.

Area of Science:

• Mechanical Engineering
• Aerospace Engineering
• Sensor Technology

Background:

• Hemispherical resonator gyros (HRGs) offer high precision, reliability, and longevity, crucial for aerospace and navigation.
• Frequency splitting, caused by resonator imperfections, is a primary error source limiting HRG accuracy.
• Structural design, particularly the equivalent bottom angle, significantly influences frequency splitting.

Purpose of the Study:

• To suppress frequency splitting in planar-electrode-type HRGs by optimizing structural parameters.
• To theoretically analyze and simulate the effect of the equivalent bottom angle on resonator vibration modes.
• To determine optimal structural parameters for enhanced HRG accuracy and performance.

Main Methods:

• Thin shell theory applied to model the 4-antinode vibration mode and waveform precession.
• Theoretical analysis and simulation of the equivalent bottom angle's effect on vibration mode frequency under various boundary conditions.
• Central composite design used to optimize equivalent bottom angle parameters (stem diameter D, fillet radii R1, R2) with frequency value and mass sensitivity as responses.

Main Results:

• The equivalent bottom angle influences the 4-antinode vibration mode through radial constraints.
• Optimized parameters (D=7 mm, R1=1 mm, R2=0.8 mm) yielded a 4-antinode vibration mode frequency of 5441.761 Hz.
• The optimized design achieved a mass sensitivity factor of 3.91 Hz/mg, meeting working and excitation requirements.

Conclusions:

• Optimizing the equivalent bottom angle and related structural parameters effectively suppresses frequency splitting in HRGs.
• The study provides a validated method for improving HRG accuracy through structural design optimization.
• Findings offer guidance for the development of more precise and reliable inertial navigation systems.