Mode ordering in tuning fork structures with negative structural coupling for mitigation of common-mode g-sensitivity

This paper reports a method of mode ordering in tuning fork structures, effectively inducing a negative coupling stiffness between the resonant proof masses. The coupling mechanism selectively stiffens the undesirable in-phase resonance mode and softens the desirable out-of-phase resonance, thus widening the frequency separation between the desirable and undesirable modes of vibration in tuning fork structures. In gyroscopes, the approach leads to improved robustness to fabrication imperfections and immunity to environmental vibrations, while at the same time enhancing the scale factor and reducing the noise. Advantages of the method are illustrated on a Quadruple Mass Gyroscope (QMG) architecture, which was previously reported. It is experimentally demonstrated that the common-mode g-sensitivity can be reduced by over 20 times with design modifications resulting in mode re-ordering.