Theoretical Investigation on Cross-Coupling Effect of Two-Dimensional Compound Pendulum Tiltmeter

Abstract

The active vibration isolation of low-frequency tilt is important for precise scientific measurement. However, the cross-coupling effects in tilt sensitive probes introduce negative effects on the performance of active isolation devices. In this paper, we show the structure and basic principle of compound pendulum (CP)-type tiltmeter, and analyze the dynamic response of the CP to the two-dimensional tilt vibrations. Besides, we deduce theoretically the mathematical model of the capacitive sensing of the displacements of the CP. Finally, we evaluate numerically the cross-coupling effects of a tilt sensitive probe including the cross-couplings of dynamic response and the different capacitance variations in two orthogonal degrees of freedoms. The maximum of the mechanical dynamic coupling factor is less than −60[Formula: see text]dB. The total cross-coupling coefficients including the different capacitance variations of the probe are both less than [Formula: see text]. Therefore, the cross-coupling effects don’t have to be considered for this kind of two-dimensional tilt sensitive probe.