Torque-Dependent Anchor Loss and Fourth-Harmonic Damping Anisotropy in Coriolis Vibratory Gyroscopes

The quality factor (Q) and its circumferential non-uniformity are essential for the resolution and long-term stability of Coriolis vibratory gyroscopes (CVGs). In practice, packaging and mounting anchors introduce torque-dependent and circumferentially non-uniform anchor dissipation, resulting in harmonic damping anisotropy. This paper presents an energy-consistent framework that quantitatively relates the tightening torque to both the mean damping factor η=1/Q and its circumferential harmonic components. A hemispherical resonator gyroscope (HRG) is used for validation, where the dominant component is the fourth harmonic. By decomposing the energy dissipated per cycle, anchor loss is separated into friction loss and radiation loss. The friction channel is modeled using a partial-slip contact energy loss formulation combined with an equivalent tangential impedance coupling description, leading to a torque power-law scaling suitable for parameter identification. The radiation channel is described by an impedance coupling model that captures torque-enhanced anchor stiffness and potential saturation leakage under strong coupling. Controlled torque experiments show that η(ϑ) exhibits an almost pure fourth-harmonic dependence on the standing wave orientation for all tested torques. Within the accessible torque range, the mean damping decreases slightly with torque, while the harmonic amplitude increases and the phase progressively converges, supporting a friction-dominated interpretation. The phase convergence further suggests progressive stabilization of the contact state. The proposed approach provides quantitative guidance for torque selection and anchor structure design in resonant gyroscopes.